Final answer:
The side lengths of the triangle formed by points T(2, 0), U(6, -3), and V(7, 4) are 5 units, approximately 7.071 units, and approximately 6.403 units when calculated using the distance formula based on the Pythagorean theorem.
Step-by-step explanation:
The points T(2, 0), U(6, -3), and V(7, 4) form a triangle, and we are asked to find the side lengths of this triangle. To calculate these lengths, we will use the distance formula which is derived from the Pythagorean theorem. Here's how you would calculate each side:
- To find the length between points T and U, known as TU, you use the distance formula: distance = √[(x2 - x1)² + (y2 - y1)²]. Plugging in the coordinates, you get: TU = √[(6 - 2)² + (-3 - 0)²] = √[16 + 9] = √25 = 5 units.
- Next, for the length between points U and V, known as UV, you apply the same formula: UV = √[(7 - 6)² + (4 - (-3))²] = √[1 + 49] = √50 = approximately 7.071 units.
- Lastly, for the length between points V and T, known as VT, you again use the distance formula: VT = √[(7 - 2)² + (4 - 0)²] = √[25 + 16] = √41 = approximately 6.403 units.
Therefore, the side lengths of triangle TUV are 5 units, approximately 7.071 units, and approximately 6.403 units, respectively.